What is Sampling? What is Sampling Theorem?

Sampling Theorem

 

Sampling refers to the process of converting a continuous-time signal into a discrete-time signal by measuring the amplitude of the signal at regular intervals of time. In other words, it involves taking snapshots of the signal at specific time intervals. This process is necessary when we want to process or transmit a continuous-time signal using digital devices or systems.

The sampling theorem, also known as the Nyquist-Shannon sampling theorem, is a fundamental concept in digital signal processing that states that a continuous-time signal can be perfectly reconstructed from its samples if the sampling frequency is greater than or equal to twice the maximum frequency present in the signal, which is also known as the Nyquist frequency. Mathematically, the theorem can be stated as:

"If a continuous-time signal x(t) contains no frequencies higher than B Hz, then it is completely determined by a set of samples taken at uniform intervals of 1/(2B) seconds."

In other words, the theorem provides a condition for perfect reconstruction of a continuous-time signal from its samples, which is essential for digital signal processing applications.